# SIGNAL DE NOISING METHOD BASED ON AUTOCORRELATION COEFFICIENT

Document Type:Dissertation

Subject Area:Technology

The advances in the innovation of simple to-computerized transformation (ADC) and the other way around, and ongoing improvements in advanced flag handling (DSP) empower simple extraction and de-noising of signs. For instance, ecological estimations completed in submerged zones, for example, in the sea clearly require signals which are free from undesirable backscatter and mess. Evacuating the undesirable parts of this flag typically sums to applying some type of separating strategy like even a high pass channel, a band pass channel, a Wiener channel. These methodologies may not anyway be the best of the alternatives because of a few viewpoints, for example, being constrained in their capacities in expelling acoustic returns that typically change the extent that their unearthly attributes are concerned.

It is additionally realized that the information or flag estimated from this present reality condition is tainted by the commotion. The most regularly utilized flag de-noising techniques are; Channel de-noising, Fu Lye change de-noising and wavelet change de-noising. The vast majority of these de-noising techniques depend on the commotion estimation to de-clamor. The procedure of de-noising or clamor expulsion can't expel commotion totally and could even misshape the first flag. The current de-noising strategies can't likewise expel the clamor in the flag quantitatively. The area of autocorrelation is the significant space for completing the way toward securing clean flag and commotion expulsion. If the aim of the de-noising is to remove part of the noise, one should find out the noise autocorrelation coefficient.

The reduction of the value of the coefficient is close to the de-noising result of the correlation coefficient of the noise that is required to be removed. [4] Advantages of this proposed method; It effectively overcomes the existing technology due to the inability to measure the original signal noise and noise can only be de-noised according to the noise estimation value which leads to noise reduction. Disadvantages of this proposed method; Unable to quantitatively eliminate noise. Autocorrelation (of signals) Auto connection and cross relationship are essential both in signs and frameworks examination. m which may be used to implement both auto and cross correlation function. Its use is indicated in the following examples: Autocorrelation sequence of a sine wave with frequency 1 Hz, sampling frequency of 200 Hz.

N=1024; % Number of samples f1=1; % Frequency of the sine wave FS=200; % Sampling Frequency n=0:N-1; % Sample index numbers x=sin(2*pi*f1*n/FS); % Generate the signal, x(n) t=[1:N]*(1/FS); % Prepare a time axis subplot(2,1,1); % Prepare the figure plot(t,x); % Plot x(n) title('Sinwave of frequency 1000Hz [FS=8000Hz]'); xlabel('Time, [s]'); ylabel('Amplitude'); grid; Rxx=xcorr(x); % Estimate its autocorrelation subplot(2,1,2); % Prepare the figure plot(Rxx); % Plot the autocorrelation grid; title('Autocorrelation function of the sinewave'); xlabel('lags'); ylabel('Autocorrelation'); Application of Correlation Functions in System Analysis Theorem: For a linear time-invariant system: The cross correlation of the output,y(n) and the input, x(n) [i. e. R yx ( m )] is equal to its impulse response when the input is white noise.

About signal processing Flag handling is a wide building discipline which manages the extraction, control and capacity of information and data which might be installed in complex-organized flags and pictures. The thought of "flag handling" may now and again appear to be something that is much perplexing. All things considered, the truth of the matter is that the greater part of the flag handling strategies and prepared have just been completed a few times, but in an oblivious way. Gaining, preparing and translating information, cleaning it for point by point and effective investigation and extraction of helpful data – the greater part of this is the thing that exploratory science is about. What's more, by giving all the more smart thoughts of displaying and calculations, one can touch base at an outfit of techniques that constitutes a logical train in its own particular right.

The massive advances in programming building since the 1960s have been instrumental in the exponential change of banner planning. The reliably creating power of PCs made it possible to execute, logically, more present day game plans. In fact, even without being totally aware of its concealed closeness, signal taking care of is at the center of our consistent everyday presence and moreover of fundamental intelligent advances. [8] For example, a mobile phone is a consider hail getting ready, working various limits that empower us to confer, exchange or store vocal messages, music and pictures or accounts. (Without a doubt, record measures, for instance, MP3, jpeg, mpeg, and various others are unadulterated banner getting ready things. These new designs can lead flag handling to re-develop itself, regarding procedures from conveyed processing, streamlining or machine learning.

However flag handling must keep its personality and specificities, and assurance the improvement of techniques that are both generalizable and computationally productive. It should likewise be founded on an inside and out comprehension of information and be generally mindful of its potential effect on our general public. Image processing Image processing is a method to perform some operations on an image in order to get an enhanced image or to extract some useful information from it. Many studies have revolved around signal de-noising and receive positive results. This filter works by applying a mask over every pixel in the image signal. Each of the components of the pixels come under the mask that is being averaged together in order to form a single pixel.

The mean filter can be defined as; X1 and x2 denotes the range of pixels in the image that is being processed. This filter is most suitable and useful for removing grain noise from the photography image. As every pixel is being summed the mean of the pixels in the neighborhood is worked out, the local variations that are brought about by grain noise are reduced considerably by being replaced by an average value. A one dimensional Gaussian function can be expressed as follows Denotes the standard deviation of the distribution, which is assumed to have a mean value of 0. Gaussian function is used to define the probability distribution of noise or data. Proposed methods for speech recognition enhancement in noisy conditions at autocorrelation domain Autocorrelation mel-frequency cepstral coefficients (AMFCC) method In this approach the MFCC coefficients are extracted from the noisy speech signal autocorrelation sequence after removing some of its lower lag coefficients.

These lower lag coefficients appear to have the highest influence on the noisy speech signal for many noise types, including those with least correlations among frames. The lag threshold value used is about 3 ms and is set by finding the first valley in the absolute autocorrelation function found over TIMIT speech frames. Since the noise spectrum may, in many occasions, be considered flat in comparison to the speech spectrum, the differentiation either reduces or omits these relatively flat parts of the spectrum, leading to even further suppression of the effect of noise. The final stages included applying the resultant magnitude of the differentiated autocorrelation-derived power spectrum to a conventional mel-frequency filter bank and passing the logarithm of the outputs to a DCT block to extract a set of cepstral coefficients per frame.

In fact, the SPFH method tried to attenuate the effect of noise after preserving higher lags of noisy autocorrelation sequence by high-pass filtering, and preserving spectral peaks, as in equation similar to DAS. Autocorrelation-based noise subtraction (ANS) method As an ideal assumption, we can consider the autocorrelation of noise as a unit sample at the origin and zero at other lags. Therefore, that portion of noisy speech autocorrelation sequence which is far enough from the origin will have the same autocorrelation as clean speech signal. The average autocorrelation of a number of non-speech frames of the utterance is used as an estimate of the noise autocorrelation sequence. We write this as Consideration of cross-correlation term in noisy speech recognition One should expect the clean speech signal and noise, in most circumstances, to be completely uncorrelated.

However, the autocorrelation sequence of the noisy speech signal is not equal to the sum of those of clean speech and noise. In order to be able to have a more accurate estimate of the clean speech signal autocorrelation, one needs to consider some correlation among clean speech and noise signals to compensate for this difference. It should be noted that this difference is in fact due to the short-time nature of our analysis, as the simple form of additive autocorrelation is only possible when an infinitely long. In fact, problems associated with non-linearity are not encountered anymore, and inaccuracies in speech spectral estimates are only due to errors in noise autocorrelation estimation and its associated problems. The power spectra of a frame of an utterance of the word “one”, uttered by a female speaker and contaminated with train station noise at 0 and 10 dB SNRs.

This utterance is extracted from test set A of the Aurora 2 task. The power spectra of signal after the application of ANS and spectral subtraction are shown. As it is clear, the power spectrum extracted after the application of ANS to the noisy speech closely follows the peaks and valleys of the clean spectrum while the SS-treated one has a more different appearance. When wavelets which were meant for the whole real axis are used, the consequences are structural delay and, which can be large. Illustration in MAT LAB Wavelets are able to localize the features in a set of data to different scales and thus the important signals can be preserved while removing noise. The idea behind the method of wavelet de-noising is that the wavelet leads to a sparse representation for many real-world signals.

The wavelet transform concentrates the features of the signal in a few wavelet coefficients that are of large magnitudes. The wavelet coefficients which are small is magnitude or value are typically the noise and they can thus be shrinked or removed without interfering with signal quality. [13] The method is based on the auto-correlation coefficient of de-noising results, and it is independent of de-noising algorithms and tools and de-noising process. Wavelet De-noising Method for Selecting Decomposition Levels and Noise Thresholds Another technique has been introduced to de-clamor 1-D test signals utilizing wavelet changes. In spite of the fact that the cutting edge wavelet de-noising techniques perform superior to anything other de-noising strategies, they are not extremely viable for trial signals. Dissimilar to pictures and different signs, test motions in substance and biophysical applications for instance, are less tolerant to flag mutilation and under-de-noising caused by the standard wavelet de-noising strategies.

The new strategy gives a technique to choose the quantity of decay levels to de-commotion, utilizes another equation to ascertain clamor edges that does not require commotion estimation, utilizes isolate commotion limits for positive and negative wavelet coefficients, applies de-noising to the Approximation segment, and enables the adaptability to change the clamor edges. Take the inverse discrete wavelet transform (IDWT) of the resultant k Detail components and the kthApproximation component. Limitations of Current Shrinkage Methods The choice of k, the number of decomposition levels to be de-noised, is arbitrary. The choice of σ Noise∼ greatly influences the noise threshold λ, but there is no definitive way to estimate the noise value σ Noise∼. Although widely used, different noise estimates yield different noise thresholds Expecting white Gaussian clamor (WGN), a solitary commotion edge is chosen and connected to the sizes of both the negative and positive Detail coefficients.

Other commotion, for example, Poisson clamor, Rician clamor, and reasonable clamor are not considered for positive or negative predisposition in commotion. In the new technique, the client decides the Detail segments to be de-noised with the assistance of visual connection. A simple path is to choose decay levels until the point when one is come to in which clamor is relatively undefined. The area and greatness of flag and commotion in the wavelet part are likewise helpful wellsprings of data, particularly to identify efficient clamor. In all the Detail parts, signals happen in similar areas with extensive sizes, while arbitrary clamor shows up conflictingly with little extents, and deliberate commotion normally happens at a particular area with low greatness. The measure of commotion show in the Detail parts lessens from deterioration level 1 to decay level M since clamor as a rule contains more high frequencies than low frequencies.

This subjective technique is valuable when a solitary arrangement of exploratory information should be de-noised. It gives control to the experimentalist in choosing the disintegration levels and additionally experiences about the flag watched for examination 1-D Double-Density Thresholding Method Thresholding is a strategy utilized for flag and picture de-noising. The discrete wavelet change utilizes two sorts of channels averaging channels, and detail channels. When we decay a flag utilizing the wavelet change, we are left with an arrangement of wavelet coefficients that connects to the high recurrence sub-groups. These high recurrence sub-groups comprise of the subtle elements in the informational index. Noisy 1-D Signal. The accompanying segment of MATLAB code demonstrates to change over a picture to a twofold information compose (for similarity with MATLAB), how to make a boisterous flag, and show the de-noised motion in the wake of applying the 1-D twofold thickness DWT strategy.

Note that we utilize a limit estimation of 25, which is the ideal edge point for this case. Afterward, we will represent how to locate the ideal edge esteem. Example (noise removal using the 1-d double-density dwt method) >> s1 = double(imread('peppers. We can see that 1-D complex twofold thickness strategy evacuates more clamor motion than 1-D twofold thickness technique does. This can be demonstrated by the "RMS Error versus Edge Point" plot, which is demonstrated as follows. RMS Error vs. Threshold Point Comparison Between Double-Density DWT And Double-Density Complex DWT De-noising Methods. We can likewise observe where the ideal edge point esteem lies. These sensor placed at any location may have some noise. For the real time application it is also affected by the various types of noise.

Here the noise being considered is the transient noise. Many researchers have work in this field based on the autocorrelation based methodologies. In 1981 one presented a linear prediction technique (LPT) for broadcast, analysis and recognition. The single slack autocorrelation minimization (SLAM) calculation is utilized to decay clamor with shortening sign to commotion proportion (SSNR) as a ceasing measure. A progressed otherworldly subtraction is utilized to limit clamor, in view of cross-connection between's the required flag and commotion motion for the standardization of mean and change of vitality and focal parameter. Another relationship coefficient that is Pearson connection coefficient based methods are likewise presented. Benesty displayed the squared Pearson relationship coefficient (SPCC) based cost work for commotion decrease system. The commotion decay worried about the SPCC-based cost work gives a more proper standard to streamlining and acquaints another parameter contrasted and the MSE.

It utilizes the base fluctuation mutilation less reaction (MVDR) [14] approach. These above models drive appropriately the between outline connection of the discourse and commotion signals. It requires the examination of their measurements on an expansive dataset is processed. The use of one space motions in the Global Positioning System (GPS) is extremely normal. The auto (cross) connection properties of codes utilized as a part of GPS and impact of clamor on code relationship have the immense effect on the correspondence. The transient noise problem is reduced through the autocorrelation function. The noise reduction is performed by considering constant mean to recover the signal of interest s (k) (clean speech) from the noisy signal observation (microphone signal) S (k) = s (k) + n (k) Where n (k) is the unwanted additive transient noise which is assumed to be a zero-mean random process (white or colored) and uncorrelated with.

An estimate of s (k) can be obtained by passing S (k) through a linear filter. Representing the finite impulse response (FIR) of length L, superscript T represents the transpose of the vector. With this formulation, the objective of noise reduction is to find an optimal filter that would attenuate the noise as much as possible while keeping the distortion of the clean speech low. The autocorrelation function for the speech signals, using the finite window of length N-1, at time index "n", the "k"th lag is: (a) Shows the autocorrelation of a speech sample signal (b) Shows the correlation of a music sample signal Where The analyses from figure (a) is that the speech signals have the second peaks are approximately one fourth of the highest peak.

And for the musical signals the second peaks are approximately half of the highest peak. The autocorrelation coefficient is maintained up to 25-35 percent for the speech signal from its second peak at zero delay and up to 45-50 percent for the musical signal except for the zero time delay lag. The iterative median filtering is used for the autocorrelation as constraint. The median filtering smoothening is applied to eliminate speech like noise components of the speech signal. We will discuss these two groups of methods separately. Autocorrelation amplitude-based approaches Calculation of the autocorrelation for noisy signal Assuming v (m, n) to be the additive noise, x (m, n) noise-free signal and h (n) impulse response of the channel, then the noisy signal y(m,n) can be written as Y (m, n) =x (m, n) ∗h (n) +v (m, n) …(1) Where * denotes the convolution operation, N is the frame length, n is the discrete time index in a frame, m is the frame index and M is the number of frames.

If x (m, n), v (m, n) and h (n) are considered uncorrelated, the autocorrelation of the noisy speech can be expressed as ………………. (2) Where ryy(m,k) , rxx(m,k) and rvv (m, k) are the short-time autocorrelation sequences of the noisy signal, clean signals and noise respectively and k is the autocorrelation sequence index within each frame. Since additive noise is assumed to be stationary, its autocorrelation sequence can be considered the same for all frames. These techniques utilize either sufficiency or stage in the autocorrelation space, as talked about above DAS algorithm This approach joins the benefits of RAS and DPS. In this calculation (part the discourse motion into outlines and applying a pre-accentuation channel, the autocorrelation grouping of the casing signal is acquired utilizing either a fair or a one-sided estimator.

A FIR channel is then connected to the uproarious flag autocorrelation arrangement. Hamming windowing and brief time Fourier change constitute the following stages. At that point, the differential power range of the sifted flag is figured. At that point, an AGC (Automatic Gain Control) was connected to the channel yields. Level when the levels of information change. In this way, the contributions underneath 30 dB are opened up directly by 20dB and contributions over 30 dB are enhanced progressively less. In the wake of finding the disconnected pinnacles, the pinnacles were strung together and smoothed. At that point three pinnacle frequencies and two pinnacle subordinates were found and added to the element vector. In each case the properties of the noise are different, as are the image processing operations that can be applied to reduce their effects.

Mat lab code for image de-noising s1 = double(imread('peppers. jpg')); s = s1(:,:,3); figure(1) imagesc(s) colormap(gray) axis image title('Original Image') x = s + 20*randn(size(s)); figure(2) imagesc(x) colormap(gray) axis image title('Noisy Image') T = 15; y = double_S2D(x,T); figure(3) imagesc(y) colormap(gray) axis image title('Denoised Image') close all clear clc a3=imread('1','jpg'); a2=rgb2gray(a3); b=imresize(a2,[256 256]); th='s'; b=double(b)+40*rand(size(b)); [a1,b1,c1,d1]=dwt2(b,'db2'); imshow(b1) [a2,b2,c2,d2]=dwt2(a1,'db2'); [a3,b3,c3,d3]=dwt2(a2,'db2'); v1=(median(abs(b3(:)))/0. 6745); b3= wthresh(b3,th,v1); v2=(median(abs(c3(:)))/0. 6745); c3= wthresh(c3,th,v2); v3=(median(abs(d3(:)))/0.

e. there are some correlation between the surrounding pixels. % % Philippe Magiera & Carl Lndahl, 2008 % function A = ROFdenoise(Image, Theta) [Image_h Image_w] = size(Image); g = 1; dt = 1/4; nbrOfIterations = 5; Image = double(Image); p = zeros(Image_h,Image_w,2); d = zeros(Image_h,Image_w,2); div_p = zeros(Image_h,Image_w); for i = 1:nbrOfIterations for x = 1:Image_w for y = 2:Image_h-1 div_p(y,x) = p(y,x,1) - p(y-1,x,1); end end for x = 2:Image_w-1 for y = 1:Image_h div_p(y,x) = div_p(y,x) + p(y,x,2) - p(y,x-1,2); end end % Handle boundaries div_p(:,1) = p(:,1,2); div_p(:,Image_w) = -p(:,Image_w-1,2); div_p(1,:) = p(1,:,1); div_p(Image_h,:) = -p(Image_h-1,:,1); % Update u u = Image-Theta*div_p; % Calculate forward derivatives du(:,:,2) = u(:,[2:Image_w, Image_w])-u; du(:,:,1) = u([2:Image_h, Image_h],:)-u; % Iterate d(:,:,1) = (1+(dt/Theta/g).

*abs(sqrt(du(:,:,1). ^2+du(:,:,2). The de-noising performance of all considered methods are compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of L2 distances of the de-noised version to the original image. The most powerful evaluation method seems, however, to be the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method. The result obtained by simulation is illustrated through the following mentioned figures. The spectrum is having no significant component above the 7 KHZ frequency. Determining synchronization pulses: The synchronization pulses in a received signal, which in turn facilitates the process of data retrieval at the receiver's end.

This is because the correlation of the known synchronization pulses with the incoming signal exhibits peaks when the sync pulses are received in it. This point can then be used by the receiver as a point of reference, which makes the system understand that the part of the signal following from then on (until another peak is obtained in the correlated signal indicating the presence of sync pulse) contains data. Radar engineering: Correlation can help determine the presence of a target and its range from the radar unit. When a target is present, the signal sent by the radar is scattered by it and bounced back to the transmitter antenna after being highly attenuated and corrupted by noise. The same definition holds good even in the case of signals.

That is, correlation between signals indicates the measure up to which the given signal resembles another signal. In other words, if we want to know how much similarity exists between the signals 1 and 2, then we need to find out the correlation of Signal 1 with respect to Signal 2 or vice versa. REFERENCES [1] S. Ikbul, H. Buhong “Auto-correlation Property of Speech and Its Application in Voice Activity Detection” International Workshop on Education Technology and Computer Science 2009, pp. [4] G. Faraham, S. M. Ahadi, and M. [7] Y. Hu , M. Bhatnagar and P. C. Loizou, “A crosscorrelation technique for enhancing speech corrupted with correlated noise” IEEE 2001, pp. on Audio, Speech, and Language Process. , vol. 16, no. 4, May 2008, pp. [10] T. 1, Jan. 2012, pp. [12] A. Schasse and R. Martin, “Online inter-frame correlation estimation methods for speech Enhancement in frequency subbands” IEEE, ICASSP 2013, pp.

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